A necessary and sufficient condition for Ricci shrinkers to have positive AVR
HTML articles powered by AMS MathViewer
- by Bennett Chow, Peng Lu and Bo Yang PDF
- Proc. Amer. Math. Soc. 140 (2012), 2179-2181 Request permission
Abstract:
In this short paper we observe that a recent result of C.-W. Chen meshes well with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L. Ni, and S.-J. Zhang. We give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci solitons to have positive asymptotic volume ratio.References
- Huai-Dong Cao and Detang Zhou, On complete gradient shrinking Ricci solitons, J. Differential Geom. 85 (2010), no. 2, 175–185. MR 2732975
- Carrillo, José A., Ni, Lei, Sharp logarithmic Sobolev inequalities on gradient solitons and applications. Communications in Analysis and Geometry 17 (2009), 721–753.
- Bing-Long Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009), no. 2, 363–382. MR 2520796
- Chen, Chih-Wei, On the injectivity radius and tangent cones at infinity of gradient Ricci solitons. arXiv:1012.1217.
- Fu-quan Fang, Jian-wen Man, and Zhen-lei Zhang, Complete gradient shrinking Ricci solitons have finite topological type, C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 653–656 (English, with English and French summaries). MR 2423272, DOI 10.1016/j.crma.2008.03.021
- Haslhofer, Robert, Müller, Reto, A compactness theorem for complete Ricci shrinkers. arXiv:1005.3255v2.
- Munteanu, Ovidiu, The volume growth of complete gradient shrinking Ricci solitons. arXiv:0904.0798.
- Zhang, Shijin. On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below. arXiv:0909.0716, Acta Mathematica Sinica 27, no. 5 (2011), 871–882.
Additional Information
- Bennett Chow
- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
- MR Author ID: 229249
- Email: benchow@math.ucsd.edu
- Peng Lu
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
- MR Author ID: 308539
- Email: penglu@uoregon.edu
- Bo Yang
- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
- Email: b5yang@math.ucsd.edu
- Received by editor(s): February 2, 2011
- Published electronically: September 30, 2011
- Communicated by: Jianguo Cao
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2179-2181
- MSC (2010): Primary 53Cxx
- DOI: https://doi.org/10.1090/S0002-9939-2011-11173-0
- MathSciNet review: 2888203